An Adaptive Finite Element Method for the LaplaceBeltrami Operator on Implicitly Defined Surfaces
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We present an adaptive finite element method for approximating solutions to the Laplace-Beltrami equation on surfaces in ℝ3 which may be implicitly represented as level sets of smooth functions. Residual-type a posteriori error bounds which show that the error may be split into a "residual part" and a "geometric part" are established. In addition, implementation issues are discussed and several computational examples are given. © 2007 Society for Industrial and Applied Mathematics.
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